Related papers: Flexible Weinstein manifolds
This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.
This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi…
We introduce a class of Weinstein domains which are sublevel sets of flexible Weinstein manifolds but are not themselves flexible. These manifolds exhibit rather subtle behavior with respect to both holomorphic curve invariants and…
In this paper, we introduce the notions of an iterated planar Lefschetz fibration and an iterated planar open book decomposition and prove the Weinstein conjecture for contact manifolds supporting an open book that has iterated planar…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
In this note we observe that while all overtwisted contact structures on compact 3--manifolds are supported by planar open book decompositions, not all contact structures are. This has relevance to invariants of contact structures and also…
We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact…
We give an elementary topological obstruction for a manifold $M$ of dimension $2q{+}1 \geq 7$ to admit a contact open book with flexible Weinstein pages and $c_1(\pi_2(M)) = 0$: if the torsion subgroup of the $q$-th integral homology group…
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
Some geometric structures with associated Riemannian metrics have been considered in the book.
In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.
We show that a stabilized convex symplectic (also called Liouville) manifold with the homotopy type of a half dimensional CW-complex is symplectomorphic to a flexible Weinstein manifold.
We introduce a canonical outer vector field on a Poisson manifold, also due independently to A. Weinstein. We view it as a global section of the sheaf of Poisson vector fields modulo the subsheaf of hamiltonian vector fields. We study this…
This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.
According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…
We show the existence of a contractible periodic Reeb orbit for any contact structure supported by an open book whose binding can be realised as a hypersurface of restricted contact type in a subcritical Stein manifold. A key ingredient in…